Method and apparatus for wheel alignment

ABSTRACT

A vehicle wheel alignment method and system is provided. A three-dimensional target is attached to a vehicle wheel known to be in alignment. The three-dimensional target has multiple target elements thereon, each of which has known geometric characteristics and 3D spatial relationship with one another.

BACKGROUND

1. Field of Invention

The teaching presented herein relates to a method and apparatus fordetermining the alignment of vehicle wheels. More specifically, theteaching relates to a method and apparatus for determining the alignmentof vehicle wheels using a three-dimensional target.

2. Discussion of Related Art

It is commonly known that if the wheels of a vehicle are out ofalignment with each other, it can result in excessive or uneven wear ofthe tires and/or adversely affect the handling and stability of thevehicle. Therefore, the wheels of a vehicle need to be periodicallychecked to determine whether they are in alignment. Conventionally, todetermine the alignment of wheels, a two-dimensional target is mountedonto the wheel to facilitate wheel alignment. A conventionaltwo-dimensional target 100 is shown in FIG. 1 (PRIOR ART). Theillustrated two-dimensional target 100 is a planar object 105 having aplurality of target elements 120 spatially arranged in a known patternon the object surface 110. The target elements 120 may be maderetro-reflective and the object surface 110 may be non-reflective toprovide suitable contrast.

The two-dimensional target 100 can be used to facilitate wheelalignment, which is disclosed in U.S. Pat. Nos. 5,535,522 and 5,809,658.A wheel alignment system (as illustrated in FIG. 9 of U.S. Pat. No.5,809,658) may be deployed in which a camera may be set up to capture atwo-dimensional image of the two-dimensional target 100, in which thetarget elements 120 on the two-dimensional target 100 are visible.Certain features relating to the target elements may be computed byprocessing the captured two-dimensional image and such features can beused to determine the alignment of the wheel to which thetwo-dimensional target is attached using techniques well know in thewheel alignment art.

One problem associated with use of a two-dimensional target for wheelalignment is that a two-dimensional target of a large size is needed inorder to achieve accurate wheel alignment determination.

SUMMARY

The need to achieve accurate measurement such as wheel alignmentdetermination is addressed by the present teaching. The present teachingprovides an improved system using a 3D target.

One aspect of the present teaching relates to a method for determiningthe alignment of a motor vehicle wheel. A three-dimensional target isattached on the vehicle wheel, where the three-dimensional target hasthereon a plurality of target elements that have certain known geometriccharacteristics and are configured in 3D space in accordance withcertain known three-dimensional relationships with each other. Aplurality of target element images corresponding to the plurality oftarget elements are detected from a 2D image of the three-dimensionaltarget acquired by at least one camera. The alignment of the wheel isdetermined based on a spatial orientation of the three-dimensionaltarget determined based on the target element images and thethree-dimensional relationships among the target elements.

According to one embodiment, a three-dimensional target is attached on avehicle, where the three-dimensional target has thereon a plurality oftarget elements, that have certain known geometric characteristics andare configured in 3D space in accordance with known three-dimensionalrelationships with each other. A 2D image of the three-dimensionaltarget is acquired using at least one camera. The 2D image of thethree-dimensional target is used to determine wheel alignment based onthe three-dimensional target.

A different aspect of the present teaching relates to a system fordetermining the alignment of a motor vehicle wheel. A three-dimensionaltarget is used for attaching to a vehicle wheel, where thethree-dimensional target has thereon a plurality of target elements thathave certain known geometric characteristics and are configured in 3Dspace in accordance with known three-dimensional relationships with eachother. A 2D imaging system is deployed for acquiring a 2D image of thethree dimensional target. A target element feature detecting systemdetects, from the 2D image, a plurality of target element imagescorresponding to the plurality of target elements. A wheel alignmentdetermination system determines the alignment of the vehicle wheel basedon a spatial orientation of the three-dimensional target determined inaccordance with the detected target element images and thethree-dimensional relationships among the target elements.

According to one embodiment of a system for determining the alignment ofa motor vehicle wheel, a three-dimensional target is used that isattachable to a wheel to be aligned. The three-dimensional target hasthereon a plurality of target elements that have certain known geometriccharacteristics and are configured in 3D space in accordance withcertain known three-dimensional relationships with each other. Animaging system, having at least one camera, is configured capable ofacquiring a 2D image of the three dimensional target. A wheelorientation determination system is configured for utilizing the 2Dimage of the three-dimensional target to determine wheel orientationbased on the three-dimensional target.

Another aspect of the present teaching relates to a method fordetermining a measurement related to an object. In one embodiment, athree-dimensional target is associated with the object. Thethree-dimensional target has thereon a plurality of target elements thathave certain known geometric characteristics and are configured in 3Dspace in accordance with certain known three-dimensional relationshipswith each other. A plurality of target element images corresponding tothe plurality of target elements are detected from a 2D image of thethree-dimensional target acquired by at least one camera. A measurementrelating to the object is determined based on a spatial orientation ofthe three-dimensional target determined based on the target elementimages and the three-dimensional relationships among the targetelements.

BRIEF DESCRIPTION OF THE DRAWINGS

The inventions claimed and/or described herein are further described interms of exemplary embodiments. These exemplary embodiments aredescribed in detail with reference to the drawings. These embodimentsare non-limiting exemplary embodiments, in which like reference numeralsrepresent similar structures throughout the several views of thedrawings, and wherein:

FIG. 1 (PRIOR ART) shows a conventional two-dimensional target used invehicle wheel alignment;

FIGS. 2 a-2 e show exemplary constructions of three-dimensional targets,according to an embodiment of the present teaching;

FIG. 3 illustrates an exemplary configuration of an orientationdetermination system according to an embodiment of the present teaching;

FIG. 4 depicts the geometry of a wheel alignment system using athree-dimensional target, according to an embodiment of the presentteaching;

FIG. 5 depicts a high level diagram of an exemplary wheel alignmentsystem using a three-dimensional target, according to an embodiment ofthe present teaching;

FIG. 6 depicts a high level diagram of an exemplary 2D image featuredetection system, according to an embodiment of the present teaching;and

FIG. 7 is a flowchart of an exemplary process for determining wheelalignment using a three-dimensional target, according to an embodimentof the present teaching.

DETAILED DESCRIPTION

The present teaching relates to method and system that utilize a threedimensional (3D) target associated with an object to make a measurementrelated to the object via image processing of a two dimensional (2D)image of the 3D target. In some embodiments, the object corresponds to avehicle wheel. A 3D target can be mounted on the vehicle wheel thatenables accurate wheel alignment. In some embodiments, the objectcorresponds to a handheld device. A 3D target can be attached to orassociated with the device to enable ride height measurement. In someembodiments, the object corresponds to a camera. A 3D target attached orassociated with the camera can be used to enable self-calibrating.Details relating to 3D target enabled measurement based on 2D imageprocessing are provided below.

FIGS. 2 a-2 e show exemplary constructions of three-dimensional targets,according to an embodiment of the present teaching. In FIG. 2 a, athree-dimensional target 200 comprises two or more solid planes 201 and202. The two planes 201 and 202 are spatially adjacent to each other byaligning one side of each of the planes (see 200-1) and they form acertain angle 200-2. On plane 201, there are a plurality of targetelements 204 that are positioned on plane 201 in accordance with someknown spatial pattern. Each target element may possess somecharacteristics such as a shape, size, or color; and such features canbe quantitatively measured. For example, as shown in FIG. 2 a, thetarget elements correspond to solid circles. Such circles are oftentermed as fiducials or fids. The radius or centroid of each such circlemay be measured. In some embodiments, the target elements on the sameplane may be uniform. In other embodiments, the target elements on thesame plane may not be uniform.

Target elements on each plane are made visually perceptible. This may beachieved by introducing contrast between target elements and the surfaceof the plane on which they reside. As shown in FIG. 2 a, the targetelements are made darker than the background surface (the non targetelement regions) of the plane 201. In some embodiments, the targetelements and the background surface may be made of different materials.For instance, the target elements may be made retro-reflective and thebackground surface may be made non-reflective. In other embodiments, thebackground surface may be made both lighter than the target elements andnon-reflective.

In FIG. 2 a, plane 202 also has a plurality of target elements 203. Thetarget elements on plane 202 may be constructed in a manner similar tothe target elements on plane 201. For example, target elements in bothplanes 201 and 202 may possess similar characteristics, as shown in FIG.2 a. In some embodiments, plane 202 may be different from plane 201. Thetarget elements on plane 202 may have different characteristics. Inaddition, target elements on plane 202 may be arranged differently.

FIG. 2 b shows a different three-dimensional target 205, according toone embodiment of the present teaching. Three-dimensional target 205 hasan overall shape substantially similar to a rigid cube with a pluralityof facets, including top 206, front 207, left 208, bottom 209, back 210,and right 211. In a preferred embodiment, at least two of the facetshave one or more target elements thereon. As seen in FIG. 2 b, there arefour target elements on the back facet, 210-a, 210-b, 210-c, 210-d, andthere is one target element 209-a on the front facet of thethree-dimensional target 205. In this preferred embodiment, the surfacenorms of both facets having two-dimensional target elements thereon havethe same orientation. In some embodiments, the two-dimensional targetelements on both facets are arranged in a pattern so that all the targetelements are visible when perceived along certain lines of sight.Although all are visible, these target elements may or may not overlap.To allow all target elements to be visible, one of the two facets may bemade transparent, which is illustrated in FIG. 2 b where the front facetis transparent when looking in from the front facet towards the backfacet.

FIG. 2 c shows another exemplary construction of a three-dimensionaltarget 212, according to an embodiment of the present teaching. As shownin FIG. 2 c, a three-dimensional structure 214 is arranged physicallyadjacent to a plane 213 and the two form a certain spatial relationship.In some embodiments, the geometric characteristic of thethree-dimensional structure 214 is such that it has one surface thereonthat has the same spatial orientation same as the spatial orientation ofsurface 217 of the plane 213 to which the three-dimensional structure214 is attached. For example, surface 215 in FIG. 2 c has the samespatial orientation as surface 217 of the plane 213.

Within such a 3D construction, a plurality of two-dimensional targetelements, 216, 217-a, 217-b, 217-c, 217-d, are spatially arranged onboth surface 217 and surface 215 according to some pattern. In onepreferred embodiment, the two-dimensional target elements are arrangedso that all target elements are visible when viewed along a certain lineof sight. Although all are visible, these target elements may or may notoverlap. In one preferred embodiment, the line of sight is perpendicularto both surface 215 and 217. FIG. 2 c illustrates one possiblearrangement, where a plurality of target elements are arranged on plane213 around the three-dimensional structure 214 and a single targetelement is on surface 215. It should be understood that suchillustrations are merely exemplary and they do not limit the scope ofthe present teaching.

FIG. 2 d shows yet another exemplary construction of a three-dimensionaltarget 220, according to one embodiment of the present teaching. Thethree-dimensional target 220 corresponds to a three-dimensionalstructure, which has at least two layers of planes in parallel in somehollow space. As shown in FIG. 2 d, there are planes 223, 225, and 226,that are parallel to each other and they are positioned at differentlocations along an axis perpendicular to the surfaces of the planes. Oneor more of the parallel planes may be on one of the surfaces of thethree-dimensional structure 220. For example, parallel planes 225 and226 are on the front surface 221 of the 3D structure 220.

In some embodiments, each of the planes has one or more target elementsarranged thereon according to some pattern. In the illustratedembodiment as shown in FIG. 2 d, there are four target elements 223-a,223-b, 223-c, and 223-d arranged in a diamond shape on plane 223. Thereare two target elements 229-a and 229-b on plane 225 and two targetelements 230-a and 230-b on plane 226. In some embodiments, the patternin which the target elements are arranged is such that all the targetelements are visible when viewed along a certain line of sight. Thesetarget elements may or may not overlap.

FIG. 2 e shows a similar three-dimensional construct 231 as 220 (shownin FIG. 2 d) but having different types of target elements on differentplanes of the structure. For instance, as shown in FIG. 2 e, four targetelements 236-a, 236-b, 236-c, and 236-d are LEDs that are mounted on thefront surface 232 of the three-dimensional structure 231. In addition,FIG. 2 e shows a different arrangement of target elements 235-a, 235-b,235-c, 235-d, 235-e on plane 233.

An example of an orientation determination system on which the presentteaching may be implemented is illustrated in FIG. 3. The orientationdetermination system 300 includes a vision imaging system 302 having apair of fixed, spaced apart cameras 310, 312 mounted on a beam 314. Thebeam 314 has a length sufficient to position the cameras 310, 312respectively outboard of the sides of the vehicle to be imaged by theorientation determination system 300. Also, the beam 314 positions thecameras 310, 312 high enough above the shop floor 316 to ensure that thetwo target devices 318, 320 on the left side of the vehicle are bothwithin the field of view of the left side camera 110, and two targetdevices 322, 324 on the right side of the vehicle are both within thefield of view of the right side camera 312.

Target devices 318, 320, 322, 324 are mounted on each of the wheels 326,328, 330, 332 of the motor vehicle, with each target device 318, 320,322, 324 including an attachment apparatus 338. The attachment apparatus338 attaches the target device 318, 320, 322, 324 to wheel 326, 328,330, 332. An example of an attachment apparatus is described in U.S.Pat. No. 5,024,001, entitled “Wheel Alignment Rim Clamp Claw” issued toBorner et al. on Jun. 18, 1991, incorporated herein by reference.

In operation, once the orientation determination system 300 has beencalibrated, as described in U.S. Pat. Nos. 5,535,522 and 5,724,743, avehicle can be driven onto the rack 340, and, if desired, the vehiclelifted to an appropriate repair elevation. The target devices 318, 320,322, 324, once attached to the wheel rims, are then oriented so that thetarget devices face the respective camera 310, 312.

The location of the target devices 318, 320, 322, 324 relative to therim of the wheels 326, 328, 330, 332 to which the target devices areattached are typically known. Once the target devices 318, 320, 322, 324have been imaged in one position, the wheels 326, 328, 330, 332 arerolled to another position and a new image can be taken. Using theimaged location of the target devices 318, 320, 322, 324 in the twopositions, the actual position and orientation of the wheels 326, 328,330, 332 and wheel axis can be calculated by the vision imaging system302. Although the distance between the two positions varies, thedistance is often approximately 8 inches both forward and back.

FIG. 4 describes the imaging geometry 410 of a wheel alignment systememploying a three-dimensional target 412 based on a pinhole cameramodel. There are three coordinate systems: a 3D camera coordinate system422, a 2D image coordinate system 426, and a 3D target coordinate system414. The 3D camera coordinate system 422 has axes X, Y, and Z,respectively, and has its origin point O (424) as the focal point orpinhole. The 2D image coordinate system 426 is parallel to camera plane420, formed by the X and Y-axes, and perpendicular to the Z-axis. Thedistance F from the origin of the 3D camera coordinate system 422 to theorigin of the 2D image coordinate system 426 is the focal length of theimaging system 410. The 3D target coordinate system 414 has axes U₀, U₁,and U₂, respectively, defined in relation to the 3D camera coordinatesystem.

During imaging, each point on the three-dimensional target 412, e.g.,point Φ 416, denoted by Φ=(t₀, t₁, t₂), where t₀, t₁, and t₂ are thecoordinates of the point Φ in the 3D target coordinate system, i.e.components of the unit vector axes U₀, U₁, and U₂ of the 3D targetcoordinate system, is mathematically projected along vector r 418 andgoes through the pinhole O 424 and arrives at point P on the 2D imageplane 426 in the 2D image coordinate system. Such a 2D image point isdenoted as P=(c_(X), c_(Y)), where c_(X) and c_(Y) are the coordinatesof this projected point in the 2D image coordinate system. Therelationship between the 3D point Φ=(t₀, t₁, t₂) on thethree-dimensional target (expressed in terms of the 3D target coordinatesystem) and the 2D image point P=(C_(X), C_(Y)) is expressed as follows:

r=C+(t ₀ *U ₀)+(t ₁ *U ₁)+(t ₂ *U ₂)

c _(X) =F*(r·x)/(r·z),

c _(Y) =F*(r·y)/(r·z),

where r is the vector from the origin of the camera coordinate system toa point on the 3D target, C=(C_(X), C_(Y), C_(Z)) (not shown) is avector from the origin of the camera coordinate system to the origin ofthe target coordinate system, U₀, U₁, and U₂ are the orthogonal unitvector axes of the target coordinate system, defined relative to thecamera coordinate system, and x, y, and z are the unit vectors of thecamera coordinate system.

Substituting the expression of r, one can obtain the following:

r=C+(t ₀ *U ₀)+(t ₁ *U ₁)+(t ₂ *U ₂)

c _(X) =F*(C _(X)+(t ₀ *U ₀ x)+(t ₁ *U ₁ x)+(t ₂ *U ₂ x))/c _(Z),

c _(Y) =F*(C _(Y)+(t ₀ *U ₀ y)+(t ₁ *U ₁ y)+(t ₂ 8U ₂ y))/c _(Z),

c _(Z) =C _(Z)+(t ₀ *U ₀ z)+(t ₁ *U ₁ z)+(t ₂ *U ₂ z)

Assume each target element is observed in the acquired 2D image as ablob. Each such blob may be characterized by a centroid, and all thetarget elements can be denoted by measured centroid coordinates (mx_(i),my_(i)), where i is the index of a set of such centroids. Each suchpoint (i) corresponds to a target element feature point Φ on the target.

To determine the orientation of a vehicle wheel relative to a camera inan imaging system as just described, from which misalignment of thevehicle wheel may be determined, the imaging system as depicted in FIG.4 may be calibrated to derive a set of centroids corresponding toobserved target elements on a three-dimensional target employed todetermine wheel alignment.

Assume that this measured set of centroids (mx_(i), my_(i)) correspondto the projected set of points (c_(Xi), c_(Yi)) from the set of targetelements on the three-dimensional target, where i is the index of theset. To determine the orientation of the target relative to the camera,from which misalignment of a vehicle wheel mounted with athree-dimensional target as described herein may be determined, thefollowing cost function can be minimized:

ρ=Σ_(i)((c _(Xi) −mx _(i))²+(c _(Yi) −my _(i))²)

where (mx_(i), my_(i)) represents the measured centroid coordinate ofthe ith target element of the three-dimensional target mounted on avehicle wheel, measured in the 2D image acquired during wheel alignment,and coordinate (c_(Xi), c_(Yi)) represents a corresponding pointprojected from a target element on a hypothetical three-dimensionaltarget.

In some embodiments, the hypothetical three-dimensional target is a 3Dtarget model. This 3D target model has a known structure with aplurality of facets, each having a plurality of target elements. Thecentroid of each target element on the 3D target model may bemathematically projected or transformed onto a 2D image plane to yield aset of projected or model centroids. Each of such transformed modelcentroid has a coordinate or (c_(Xi), c_(Yi)). In such a scenario, themodel centroids can either be pre-stored or generated on the fly basedon a plurality of stored parameters that are relevant to thetransformation. Such parameters include camera parameters, thecoordinate system for the 3D target model, the camera coordinate system,and the relationship between the camera coordinate system and the 3Dtarget coordinate system.

The cost function ρ is a function of six independent parametersdescribing the 3D orientation of the target relative to the camera,because a coordinate (c_(Xi), c_(Yi)) represents a point projected onthe camera plane after a 3D point going through a 3D transformation withsix degrees of freedom. For example, the six degrees of freedom can berealized via six independent parameters, e.g., C_(X), C_(Y), C_(Z)corresponding to translation in X-Y-Z directions, and yaw, tilt, androll corresponding to rotations in the three dimensional space.

In minimizing the cost function ρ, the 3D coordinates of thehypothetical three-dimensional target are mathematically adjusted (viathe 6 independent parameters) so that the difference between the twosets of 2D points, (c_(Xi), c_(Yi)) and (mx_(i), my_(i)), are minimized.The adjustment made to the six independent parameters with respect to acalibrated 3D position that yields a minimum ρ representing theorientation of the target being measured.

FIG. 5 depicts a high level diagram 500 of an exemplary wheel alignmentsystem using a three-dimensional target, according to an embodiment ofthe present teaching. The vehicle wheel alignment system comprises avehicle wheel 501 mounted with a three-dimensional target 502, animaging system 505, a 3D target model 503, a target element featureidentification system 515, an optimization system 525, and anorientation determination system 545. Optionally, a wheel alignmentcorrection system 550 may also be included to correct misalignment ifsuch misalignment is detected.

In operation, the imaging system 505 is set up according to the imaginggeometry depicted in FIG. 4. The 3D target model 503 is used to generatemodel centroid coordinates (C_(Xi), C_(Yi)) 535-a based on a pluralityof system parameters such as camera parameters 535-d, the targetcoordinate system used 535-c, the camera coordinate system used 535-b,and the transformation relationship of the two.

The wheel alignment system 500 may be deployed to perform wheelalignment detection and correction thereof. When the three-dimensionaltarget 502 is mounted on the vehicle wheel 501, e.g., in accordance withthe system configuration as illustrated in FIG. 4, the 2D imaging system505 is activated to acquire a 2D image 510 of the three-dimensionaltarget 502. The target element feature identification system 515analyzes the acquired 2D image 510 to obtain features such as targetblobs, each of which corresponds to one target element, and/or centroidsof such identified target blobs or (mx_(i), my_(i)) 520.

The detected 2D image features such as centroids (mx_(i), my_(i)) aresent to the optimization system 525, which minimizes the cost function ρby adjusting the 3D position of the hypothetical three-dimensionaltarget or the 3D target model 503 with respect to six independentparameters as described herein. The adjustments made to the sixindependent parameters are then sent to the orientation determinationsystem 545 where the orientation of the target 501 is determined basedon the adjustment needed to minimize the cost function ρ. Then, thewheel alignment correction system 550 may compute the alignmentparameters and any needed correction to the alignment of the wheel basedon the measured orientation of the wheels relative to the each other andthe vehicle wheel alignment specifications stored in the database.

FIG. 6 depicts a high level diagram of the target element featureidentification system 515, according to an embodiment of the presentteaching. In this exemplary embodiment, circle target elements aredetected and a centroid for each circle target element is obtained torepresent the underlying target element. It should be understood thatthe 2D image features illustrated herein as well as the method andsystem employed herein to detect such 2D image features do not limit thescope of the present teaching. Other 2D images features may also be usedand the corresponding method and system may be designed and implementedto detect, identify and characterize those 2D image features.

The target element feature identification system 515 comprises an imagecomponent detection unit 620, a circle detection unit 630, and acentroid determination unit 640. Optionally, the target element featureidentification system 515 may also include an image pre-processing unit610. A 2D target image 510, acquired by the imaging system 505 may firstbe pre-processed by the image preprocessing system 610. Suchpre-processing may include image filtering, enhancement, or edgedetection.

The image component detection unit 620 analyzes a 2D image, either 510or from the image pre-processing unit 610, to identify meaningfulcomponents in the 2D image. Such components may include 2D regionswithin the 2D image, representing 2D blobs. Each of such blobs may beobtained by, e.g., performing some image segmentation operations. Forinstance, when the imaged target elements have distinct contrastcompared to the background, segmentation may be performed via athreshold operation with respect to the intensity of pixels to obtainindividual regions for the target elements or an overlapped versionthereof.

In some embodiments, based on the segmented image blobs, further imageanalysis may be performed to identify desired features. For example, ifit is known that target elements are circles, the circle detection unit630 may be invoked to detect boundaries of each image blob and comparesuch boundaries to the boundary shapes of such circles projected onto animage plane of an imaging system such as the one herein described.Additional analysis may be applied when there is overlap among imageblobs. In some embodiments, algorithms known in the art may be employedto detect the circle boundaries of overlapped image blobs. Such detectedcircles may be used to derive a certain representation for each circletarget element. For instance, the radius of a target element may becomputed based on such a detected circle. The projected center of adetected circle may be used as an estimate of the centroid of thecircle.

In some embodiments, centroids may be derived directly from imagecomponents detected by the image component detection unit 620. Forexample, for each image blob, algorithms known in the art may be appliedto compute a centroid coordinate based on the coordinates of all pixelswithin the image blob. In some embodiments, the centroid of an imageblob may also be derived based on the boundary points of the image blobsuch as a circle identified by the circle detection unit 630.

FIG. 7 is a flowchart of an exemplary process for determining wheelalignment using a three-dimensional target, according to an embodimentof the present teaching. At 710, a three-dimensional target is firstdesigned or constructed and such a three-dimensional target may have astructure as illustrated in any of FIGS. 2 a-2 e. The constructedthree-dimensional target can also have any other 3D construct that isappropriate for wheel alignment. At 720, a three-dimensional targetmodel (503 in FIG. 5) for the three-dimensional target is accordinglyestablished and projected 2D features of the three-dimensional targetmodel 503 are computed and stored for the purpose of determining wheelorientation based on the three-dimensional target model.

To perform wheel alignment, the constructed three-dimensional target ismounted, at 730, on a vehicle wheel according to certain geometricconstraints as described herein. A calibrated camera in the system asshown in FIG. 4 is activated to capture, at 740, a 2D image of thethree-dimensional target. Target elements on the three-dimensionaltarget are identified, at 750, from the 2D image and correspondingfeatures (e.g., centroids) of the target elements are then derived at760. Such features are used to minimize, at 770, the cost function ρ byadjusting the six independent parameters with respect to the 2Dprojected features of the three-dimensional target model 503. Theadjustment made during the optimization process is then used, at 780, tocompute the orientation of the target. At 790, the computed orientationof the target is then used to determine parameters to be used to alignthe vehicle wheel.

Below, the process of optimizing ρ is described according to anembodiment of the present teaching. The cost function ρ is a non-linearfunction of six parameters. There is no analytical solution to ρ.Therefore, its optimization usually requires an iterative process,hence, it is computationally expensive. There is a wealth of literaturerelated to such minimization procedures. For example, the well-knownleast squares approach can be employed to optimize ρ. To improve speedin wheel alignment, in some embodiments of the present teaching, arevised optimization process is employed.

In such a revised optimization process, the six independent parametersare separately adjusted. Thus at each step of the optimization, only oneof the six parameters is considered a variable, and the other fiveparameters are treated as constants. In this case, the cost function ρis still a non-linear function (a sum of ratios of polynomials) with noanalytical solution. In some embodiments, the optimization with respectto one parameter may be carried out iteratively. In this case, each ofthe six parameters is adjusted, in a separate process, to minimize thecost function ρ until the changes in ρ caused by the adjustment issmaller than some threshold.

In some embodiments, the cost function with one parameter may beapproximately solved. When the current parameter values are close to thevalues that minimize the cost function, the cost function ρ with oneparameter is approximately a parabolic function with a differentiable,smoothly varying functional curve. Assume a parabolic or quadraticfunction in one parameter is expressed as: ρ(q)=a*q²+b*q+c, where q is aparameter (one of the six independent parameters). The first and secondderivatives of this function correspond to: ρ′(q)=2a*q+b and ρ″(q)=2a.It is known that a minimum of ρ(q) occurs at q=q* when the firstderivative of ρ(q) with respect to q is zero. That is, ρ′(q)=2a*q+b=0.Solving this equation, q*=−b/(2*a). Since ρ′(q=0)=b and ρ″(q=0)=2a,therefore, q*=−(ρ′(0)/ρ″(0)). In this way, the parameter value q* ofparameter q minimizes the one parameter cost function ρ. Here, q*corresponds to the adjustment made to parameter q in order to minimizeρ. Applying this technique to each parameter in turn, the parametervalue for each of the other five independent parameters that minimizethe cost function ρ may be obtained.

The above discussed optimization process is applied to mathematicalexpressions corresponding to a perspective projection process. In someembodiments, a non-perspective solution may also be carried out. Asdiscussed above, c_(Z)=C_(Z)+(t₀*U₀z)+(t₁*U₁z)+(t₂*U₂z). IfCz>>(t₀*U₀z)+(t₁*U₁z)+(t₂*U₂z), then c_(Z) is approximately independentof U₀z, U₁z, and U₂z. This permits an analytical computation ofparameters C, U₀, U₁, and U₂ instead of applying an iterative processsuch as a least-square fitting. Such a solution may be adequate as afinal solution, or may be used as a starting point for the perspectivecalculation, giving parameter values close to the minimum, as required.

While the inventions have been described with reference to the certainillustrated embodiments, the words that have been used herein are wordsof description, rather than words of limitation. Changes may be made,within the purview of the appended claims, without departing from thescope and spirit of the invention in its aspects. Although theinventions have been described herein with reference to particularstructures, acts, and materials, the invention is not to be limited tothe particulars disclosed, but rather can be embodied in a wide varietyof forms, some of which may be quite different from those of thedisclosed embodiments, and extends to all equivalent structures, acts,and, materials, such as are within the scope of the appended claims.

1. A method for determining the alignment of a motor vehicle wheel,comprising the steps of: attaching a three-dimensional target on thevehicle wheel, wherein the three-dimensional target comprises a firstplanar target on a first substrate and a second planar target on asecond substrate, the first and second substrates being spaced apartfrom each other, each of the first and second planar targets havingthereon a plurality of target elements having known geometriccharacteristics and being configured in 3D space in accordance withknown three-dimensional relationships with each other; detecting, from a2D image of the three-dimensional target acquired by at least onecamera, a plurality of target element images corresponding to theplurality of target elements; and determining the alignment of the wheelbased on a spatial orientation of the three-dimensional targetdetermined based on the target element images and the three-dimensionalrelationships among the target elements.
 2. The method according toclaim 1, wherein the three dimensional target has a plurality of facets,at least one of which has one or more target elements residing on thesurface of the facet.
 3. The method according to claim 2, wherein thetarget elements on a surface of a part forms a prescribed pattern. 4.The method according to claim 2, wherein surfaces of different partshaving target elements thereon have certain geometric relationships. 5.The method according to claim 2, wherein the plurality of parts areconstructed within a housing for the three-dimensional target.
 6. Themethod according to claim 1, wherein the target elements are maderetro-reflective and reside against a non-reflective surface of thethree-dimensional target.
 7. The method according to claim 1, whereinthe target elements are made non-reflective and reside against aretro-reflective surface of the three-dimensional target.
 8. The methodaccording to claim 1, wherein the step of determining the alignmentcomprises the step of detecting an image feature of each target elementimage.
 9. The method according to claim 8, wherein the image featureincludes a representative location of the target element image.
 10. Themethod according to claim 9, wherein the representative locationcorresponds to a centroid of the corresponding target element image. 11.A method for determining the alignment of a motor vehicle wheel,comprising the steps of: attaching a three-dimensional target on avehicle, wherein the three-dimensional target comprises a first planartarget on a first substrate and a second planar target on a secondsubstrate, the first and second substrates being spaced apart from eachother, each of the first and second planar targets having thereon aplurality of target elements having known geometric characteristics andbeing configured in 3D space in accordance with known three-dimensionalrelationships with each other; acquiring a 2D image of thethree-dimensional target using at least one camera; and utilizing the 2Dimage of the three-dimensional target to determine wheel alignment basedon the three-dimensional target.
 12. A system for determining thealignment of a motor vehicle wheel, comprising: a three-dimensionaltarget for attachment to a vehicle wheel, wherein the three-dimensionaltarget comprises a first planar target on a first substrate and a secondplanar target on a second substrate, the first and second substratesbeing spaced apart from each other, each of the first and second planartargets having thereon a plurality of target elements having knowngeometric characteristics and being configured in 3D space in accordancewith known three-dimensional relationships with each other; a 2D imagingsystem for acquiring a 2D image of the three dimensional target; atarget element feature detecting system for detecting, from the 2Dimage, a plurality of target element images corresponding to theplurality of target elements; and a wheel alignment determination systemfor determining the alignment of the vehicle wheel based on a spatialorientation of the three-dimensional target determined in accordancewith the detected target element images and the three-dimensionalrelationships among the target elements.
 13. The system according toclaim 12, wherein the three dimensional target has a plurality of parts,at least one of which has one or more target elements residing on asurface of the part.
 14. The system according to claim 13, wherein thetarget elements on a surface of a part forms a prescribed pattern. 15.The system according to claim 13, wherein surfaces of different partshaving target elements thereon form certain geometric relationships. 16.The system according to claim 13, wherein the plurality of parts areconstructed within a housing for the three-dimensional target.
 17. Thesystem according to claim 12, wherein the target elements are maderetro-reflective and reside against a non-reflective surface of thethree-dimensional target.
 18. The system according to claim 12, whereinthe target elements are made non-reflective and reside against aretro-reflective surface of the three-dimensional target.
 19. A systemfor determining the alignment of a motor vehicle wheel, comprising: athree-dimensional target attachable to a wheel to be aligned, whereinthe three-dimensional target comprises a first planar target on a firstsubstrate and a second planar target on a second substrate, the firstand second substrates being spaced apart from each other, each of thefirst and second planar targets having thereon a plurality of targetelements having known geometric characteristics and being configured in3D space in accordance with known three-dimensional relationships witheach other; an imaging system, having at least one camera, capable ofacquiring a 2D image of the three dimensional target; and a wheelorientation determination system configured for utilizing the 2D imageof the three-dimensional target to determine wheel orientation based onthe three-dimensional target.
 20. A method for determining a measurementrelating to an object, comprising the steps of: associating athree-dimensional target with the object, wherein the three-dimensionaltarget comprises a first planar target on a first substrate and a secondplanar target on a second substrate, the first and second substratesbeing spaced apart from each other, each of the first and second planartargets having thereon a plurality of target elements having knowngeometric characteristics and being configured in 3D space in accordancewith known three-dimensional relationships with each other; detecting,from a 2D image of the three-dimensional target acquired by at least onecamera, a plurality of target element images corresponding to theplurality of target elements; and determining the measurement relatingto the object based on a spatial orientation of the three-dimensionaltarget determined based on the target element images and thethree-dimensional relationships among the target elements.